TY - JOUR
T1 - MILP models for objective reduction in multi-objective optimization
T2 - Error measurement considerations and non-redundancy ratio
AU - Vázquez, Daniel
AU - Ruiz-Femenia, Rubén
AU - Jiménez, Laureano
AU - Caballero, José A.
N1 - Funding Information:
The authors acknowledge financial support from the Spanish “ Ministerio de Economía, Industria y Competitividad ” ( CTQ2016-77968-C3-2-P , AEI/FEDER, UE).
Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2018/7/12
Y1 - 2018/7/12
N2 - A common approach in multi-objective optimization (MOO) consists of removing redundant objectives or reducing the set of objectives minimizing some metrics related with the loss of the dominance structure. In this paper, we comment some weakness related to the usual minimization of the maximum error (infinity norm or δ-error) and the convenience of using a norm 1 instead. Besides, a new model accounting for the minimum number of Pareto solutions that are lost when reducing objectives is provided, which helps to further describe the effects of the objective reduction in the system. A comparison of the performance of these algorithms and its usefulness in objective reduction against principal component analysis + Deb and Saxena's algorithm (Deb and Saxena Kumar, 2005) is provided, and the ability of combining it with a principal component analysis in order to reduce the dimensionality of a system is also studied and commented.
AB - A common approach in multi-objective optimization (MOO) consists of removing redundant objectives or reducing the set of objectives minimizing some metrics related with the loss of the dominance structure. In this paper, we comment some weakness related to the usual minimization of the maximum error (infinity norm or δ-error) and the convenience of using a norm 1 instead. Besides, a new model accounting for the minimum number of Pareto solutions that are lost when reducing objectives is provided, which helps to further describe the effects of the objective reduction in the system. A comparison of the performance of these algorithms and its usefulness in objective reduction against principal component analysis + Deb and Saxena's algorithm (Deb and Saxena Kumar, 2005) is provided, and the ability of combining it with a principal component analysis in order to reduce the dimensionality of a system is also studied and commented.
KW - Deb and Saxena algorithm
KW - MOO objective reduction
KW - Non-Redundancy ratio
KW - PCA
KW - δ-error
UR - http://www.scopus.com/inward/record.url?scp=85046676316&partnerID=8YFLogxK
U2 - 10.1016/j.compchemeng.2018.04.031
DO - 10.1016/j.compchemeng.2018.04.031
M3 - Article
AN - SCOPUS:85046676316
SN - 0098-1354
VL - 115
SP - 323
EP - 332
JO - Computers and Chemical Engineering
JF - Computers and Chemical Engineering
ER -